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Chapter 1 - Units and Measurement deals with the measurement of different physical quantities, for example, w hen we check the temperature of water with a thermometer, we use units like Celsius to quantify the temperature. The exercises include 17 questions, numbered from 1.1 to 1.17.
For example, when you measure the length of a table with a ruler, you are using the concept of "measurement" and "units" from this chapter. A ruler gives the length in centimeters (cm) or inches.
In the CBSE board exams, a significant portion of questions are derived directly from the NCERT concepts and exercises. This is where tools like NCERT Solutions for Physics Class 11 Chapter 1, "Units and Measurement," become incredibly valuable. You’ll find detailed solutions for each question, along with important formulas from the chapter to help you prepare for class tests, assignments, homework, and exams.
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It covers the essential topics and tools that you’ll need to understand and solve the problems in Chapter 1, which will help you develop a strong foundation in units, measurement, and related concepts
(a) The volume of a cube of side 1 cm is equal to .....
(b) The surface area of a solid cylinder of radius 2.0 cm and height 10.0 cm is equal to ...
(c) A vehicle moving with a speed of
(d) The relative density of lead is 11.3. Its density is ....
Answer:
(a) We know,
The volume of a cube of side a =
Volume of cube of side 1 cm (i.e, .01 m ) =
(b) We know,
The surface area of a solid cylinder of radius r and height h =
Required area =
(c) (Tip: multiply by 5/18 to convert
Ditance covered =
(d) Density = Relative Density
(Density of water =
Density of lead=
Q 1.2 : Fill in the blanks by suitable conversion of units
(a)
b)
(c)
(d)
Answer:
(a)
(b)
(c)
(d)
Answer:
Given,
Given new unit of mass =
Similarly in terms of new units ,
(a) atoms are very small objects
(b) a jet plane moves with great speed
(c) the mass of Jupiter is very large
(d) the air inside this room contains a large number of molecules
(e) a proton is much more massive than an electron
(f) the speed of sound is much smaller than the speed of light
Answer:
The given statement is true. A dimensional quantity may be small with respect to one reference and maybe large with respect to another reference. Hence, we require a standard reference to judge for comparison.
(a) An atom is a very small object with respect to a tennis ball. (but larger than an electron!)
(b) A jet plane moves with great speed with respect to a train.
(c) The mass of Jupiter is very large as compared to an apple.
(d) The air inside this room contains a large number of molecules as compared to in your lungs.
(e) A proton is much more massive than an electron
(f) The speed of sound is less than the speed of light
Answer:
Distance between Sun and Earth = Speed of light x Time taken by light to cover the distance
Speed of light = 1 unit
Time taken by light to reach earth is 8 minute 20 seconds
Time taken =
The distance between Sun and Earth = 1 x 500 = 500 units.
Q 1.6 : Which of the following is the most precise device for measuring length :
(a) a vernier callipers with 20 divisions on the sliding scale
(b) a screw gauge of pitch 1 mm and 100 divisions on the circular scale
(c) an optical instrument that can measure length to within a wavelength of light?
Answer:
To judge which tool is more precise, we have to find out their least count. Least count defines the margin of error and hence the precision. Hence the instrument with lower least count will be more precise.
(a) Least count =
(b) Least count = pitch/ number of divisions
=
(c) least count = wavelength of light = 400nm to 700nm, that is in the range of
Therefore, the optical instrument is the most precise device used to measure length.
Answer:
Given,
Magnification of Microscope = 100
The average width of hair under the microscope = 3.5 mm
(20 observations were made to calculate the average i.e. 3.5 mm as an experimental procedure. No need in our calculations.)
(Note: When magnified, the width is 3.5 mm. Hence actual width will be less by a factor of magnification value)
The average thickness of hair =
Q 1.8 Answer the following :
(a)You are given a thread and a metre scale. How will you estimate the diameter of the thread?
(b)A screw gauge has a pitch of 1.0 mm and 200 divisions on the circular scale. Do you think it is possible to increase the accuracy of the screw gauge arbitrarily by increasing the number of divisions on the circular scale?
(c) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate than a set of 5 measurements only?
Answer:
(a) Take the thread and wrap it around the metre scale. Make sure the coils are packed closely without any space in between. If the diameter of the thread is d and number of turns obtained are n, then (n x d) corresponds to the marking on the metre scale, l.
Therefore, the diameter of the thread would be, d = l/n
(b) Theoretically, by increasing the number of divisions on the circular divisions, the value of least count decreases and hence accuracy increases.(Lower the value of least count, better will be the reading)
But practically, the number of divisions can be increased only up to a certain limit. (Also two adjacent divisions cannot be separated by a distance less than the human eye resolution!)
(c) With an increase in the number of observations, the accuracy of the experiment increases as the error is now distributed over a large range. Hence, a set of 100 measurements of the diameter is expected to yield a more reliable estimate than a set of 5 measurements.
Answer:
Given,
Area of the house in the photo =
Area of the house on the screen =
Linear magnification of the projector- screen arrangement
Q 1.10 : State the number of significant figures in the following :
(a)
(b)
(c)
(d)
(e)
(f)
Answer:
(a) The given value is
Since, the number is less than 1 , the zeros on the right to the decimal before the first non-zero integer is insignificant. So, the number 7 is the only significant digit.
(b) The value is
For the determination of significant values, we do not consider the power of 10 (Number is not less than 1). The digits 2, 6, and 4 are significant figures.
(c)The value is
For the given value with decimals, all the numbers 2, 3, 7 and 0 are significant.
(d) The value is
It has 4 significant digits.
(e) The value is
All the four digits are significant as the zeros in between two non-zero values are also significant.
(f) The value is
Same as (a), first three zeroes after the decimal is insignificant. Only 6, 0, 3, 2 are significant.
Answer:
Given,
Length, l = 4.234 m ; Breadth, b = 1.005 m; Height, h = 2.01 cm = 0.0201 m
The length has 4 significant figures
The breadth has 4 significant figures
The height has 3 significant figures (Since the number is less than 1, hence zeroes after decimal before the first non-zero integer is insignificant)
We know,
Surface area of a cuboid = 2(l x b + b x h + h x l)
=
=
=
Volume = l x b x h
=
(Note: For Multiplication The LEAST number of significant digits in any number determines the number of significant figures in the answer; i.e decided by the number of significant digits )
The area has three significant values 2, 7 and 8.
The volume has three significant values 5, 5 and 8.
Answer:
Given,
The mass of the box = 2.30 kg
and the mass of the first gold piece = 20.15 g = 0.02015 kg
The mass of the second gold piece = 20.17 g = 0.02017 kg
(a) The total mass = 2.30 + 0.02015 + 0.02017 = 2.34032 kg
Since one is the least number of decimal places, the total mass = 2.3 kg.
(Note: For addition/subtraction , the number of places after the decimal point in the answer is less than or equal to the number of decimal places in every term in the sum; i.e decided by the numbers after the decimal. )
Guess where to put the missing c.
Answer:
The relation given is
Divide both sides by
Hence, R.H.S must be dimensionless too. (After Dividing by
Therefore, the dimensional equation is
Q 1.14 : The unit of length convenient on the atomic scale is known as an angstrom and is denoted by: 1Å = 10^{-10} m$ . The size of a hydrogen atom is about 0.5Å. What is the total atomic volume in
Answer:
Radius of an Hydrogen atom = 0.5
Volume =
=
=
1 hydrogen mole contains
The volume of 1 mole of hydrogen atom =
=
Answer:
Radius of hydrogen atom = 0.5
Volume occupied by the hydrogen atom=
=
=
1 mole of hydrogen contains 6.023 x 10 23 hydrogen atoms.
Volume of 1 mole of hydrogen atom = 6.023 x 10 23 x 0.524 x 10 -30
= 3.16 x 10 -7 m 3
The molar volume is
Hence, intermolecular separation in gas is much larger than the size of a molecule.
Answer:
Our eyes detect angular velocity, not absolute velocity. An object far away makes a lesser angle than an object which is close. That's why the moon (which is so far away!) does not seem to move at all angularly and thus seems to follow you while driving.
In other words, while in a moving train, or for that matter in any moving vehicle, a nearby object moves in the opposite direction while the distant object moves in the same direction. !
Answer:
Given,
Mass of the Sun, m =
The radius of the Sun, r =
=
Density = Mass/Volume
=
Therefore, the density of the sun is in the range of solids and liquids and not gases. This high density arises due to inward gravitational attraction on outer layers due to inner layers of the Sun. (Imagine layers and layers of gases stacking up like a pile!)
Boost your understanding of NCERT Class 11 Physics Chapter 1, 'Units and Measurements,' with our collection of key formulas, diagrams, and an eBook link. This resource provides you with the essential tools to master the chapter's concepts. Access the eBook for a complete and thorough learning experience.
Physical Quantity | Unit | Dimensions |
Density | kg/m³ | M L⁻³ |
Force | Newton (N) | M L T⁻² |
Work / Energy | Joule (J = N·m) | M L² T⁻² |
Power | Watt (W = J/s) | M L² T⁻³ |
Momentum | kg·m/s | M L T⁻¹ |
Gravitational Constant (G) | N·m²/kg² | M⁻¹ L³ T⁻² |
Angular Velocity | rad/s | T⁻¹ |
Angular Acceleration | rad/s² | T⁻² |
Angular Momentum | kg·m²/s | M L² T⁻¹ |
Angular Frequency | rad/s | T⁻¹ |
Moment of Inertia | kg·m² | M L² |
Torque | N·m | M L² T⁻² |
Frequency | Hertz (Hz) | T⁻¹ |
Time Period | Second (s) | T |
Surface Tension | N/m | M T⁻² |
Specific Heat Capacity | J/(kg·K) | L² T⁻² Θ⁻¹ |
Heat / Energy | Joule (J) | M L² T⁻² |
Electric Dipole Moment | C·m | I T L |
Electric Field | V/m or N/C | M L T⁻³ I⁻¹ |
Electric Potential (Voltage) | Volt (V = J/C) | M L² T⁻³ I⁻¹ |
Electric Flux | V·m | M L³ T⁻³ I⁻¹ |
Capacitance | Farad (F = C/V) | M⁻¹ L⁻² T⁴ I² |
Electromotive Force (EMF) | Volt (V) | M L² T⁻³ I⁻¹ |
Magnetic Field | Tesla (T) | M T⁻² I⁻¹ |
Magnetic Flux | Weber (Wb = T·m²) | M L² T⁻² I⁻¹ |
Download Ebook - Formula Sheet for Physics Class 11: Chapterwise Important Formulas With Examples, Graphs, And Points
Fundamental and Derived Quantities: Fundamental quantities are the basic building blocks of measurement, like length, mass, and time. Derived quantities are made by combining these basics, such as velocity (distance/time) or force (mass × acceleration).
Units and Systems: Different systems of units are used to measure physical quantities. The most commonly used system is the International System of Units (SI), which includes units like meters for length and kilograms for mass. It's the global standard for scientific measurements.
Significant Figures: Significant figures are the digits in a measurement that you know for sure, along with one digit that’s estimated. They show how precise and accurate your measurement is, which is crucial when working with scientific data.
Errors and Their Types: Errors refer to the differences between a measured value and the true or accepted value. There are two main types: systematic errors, which affect your measurements in a consistent way (like a miscalibrated instrument), and random errors, which happen unpredictably and vary from one measurement to the next.
Rounding Off: When reporting measurements, rounding off involves dropping extra digits that don’t affect the accuracy of your result. It helps in making the numbers easier to understand without losing precision.
Dimensions of Physical Quantities : Dimensions represent the fundamental units that describe a physical quantity. They help in understanding the relationship between different physical quantities.
Each of these topics plays a crucial role in understanding the concepts of units and measurements, and mastering them is essential for solving the exercise questions effectively.
When studying the Class 11 Physics Chapter 1 exercise solutions (now Chapter 1 as per the CBSE Syllabus 2025-26), keep the following tips in mind
Also read :
The topic and subtopic of Physics Class 11 Chapter 1 exercise solutions Units and Measurement are listed below.
Section Name | Topic Name |
1 | |
1.1 | Introduction |
1.2 | |
1.3 | |
1.4 | Measurement of mass |
1.5 | Measurement of time |
1.6 | Accuracy, precision of instruments and errors in measurement |
1.7 | |
1.8 | Dimensions of physical quantities |
1.9 | Dimensional formulae and dimensional equations |
1.1 |
In Class 11 Physics Chapter 1, "Units and Measurement," measurements always need to be accompanied by a unit; without a unit, they hold no meaning. For example, when a person says the distance between his home and the nearest city is "5," this statement is meaningless unless a unit is specified, such as 5 meters, 5 centimetres, or 5 kilometres.
The NCERT Solutions for Physics Class 11 Chapter 1 begins with questions on unit conversion. These solutions provide a clear understanding of concepts like accuracy, precision, and error, which are crucial for mastering the chapter. The chapter also covers important topics such as the concepts of errors, methods for measuring errors, dimensional analysis, and significant figures. All of these topics are addressed in detail through the Class 11 Physics Chapter 1 exercise solutions, helping students grasp key concepts and solve related questions effectively.
NCERT solutions for class 11 physics chapter-wise
NCERT solutions for class 11 Subject-wise
Multiply the given value by a conversion factor that relates the two units.
The seven fundamental SI units are:
Dimensional analysis is important in physics because it helps check the correctness of equations, convert units, and understand relationships between physical quantities.
Here are the important topics in Units and Measurements:
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